In `DeltaPQR, /_PQR = 90^@, PQ = 5 cm and QR= 12 cm`. What is the radius (in cm) of the circum-circle of `DeltaPQR`?

Options

A. 6.5
B. 7.5
C. 13
D. 15

Answer

To find the radius of the circum-circle of triangle PQR, we can follow these steps:

### Step 1: Identify the triangle properties
We know that triangle PQR is a right-angled triangle with:
- Angle PQR = 90°
- Side PQ = 5 cm
- Side QR = 12 cm

### Step 2: Use the Pythagorean theorem to find the hypotenuse PR
In a right-angled triangle, the relationship between the sides is given by the Pythagorean theorem:
\[ PR^2 = PQ^2 + QR^2 \]

Substituting the known values:
\[ PR^2 = 5^2 + 12^2 \]
\[ PR^2 = 25 + 144 \]
\[ PR^2 = 169 \]

Taking the square root to find PR:
\[ PR = \sqrt{169} = 13 \text{ cm} \]

### Step 3: Calculate the radius of the circum-circle
In a right-angled triangle, the circumradius (R) can be found using the formula:
\[ R = \frac{hypotenuse}{2} \]

Here, the hypotenuse is PR:
\[ R = \frac{PR}{2} = \frac{13}{2} = 6.5 \text{ cm} \]

### Final Answer
The radius of the circum-circle of triangle PQR is **6.5 cm**.

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